Mensuration Test

Result

Mensuration Test - 14

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Weekly Quiz Competition

Question 1
1 / -0

36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is.

A
12 units

B
26 units

C
24 units

D
36 units

Solution

Option (b) is correct.
Area of rectangle is 36 units
We have,
$$ \Rightarrow 36 = 6 \times 6 $$
$$= 2\times 3 \times 3\times 2 $$
$$=4\times 9$$
Hence, the sides of a rectangle are $$4 \,cm$$ and $$9\, cm$$
Perimeter $$= 2(l+b)$$
$$=2(4+9)$$
$$ =13\times 2$$
$$= 26\, units$$
Question 2
1 / -0

The sides length of the top of square table is $$x$$. The expression for perimeter is:

A
$$4+x$$

B
$$2x$$

C
$$4x$$

D
$$8x$$

Solution

Given that
Side length of a square table $$=x$$
Perimeter of a square=$$4\times Side=4\times x=4x$$
Question 3
1 / -0

The perimeter of the rectangle whose length is $$60 \,cm$$ and a diagonal is $$61 \,cm$$ is

A
$$120 \,cm$$

B
$$122 \,cm$$

C
$$71 \,cm$$

D
$$142 \,cm$$

Solution

Rectangle $$ABCD$$ is consist two triangle.
Let triangle $$BCD$$ has two sides equal $$AD = CD = 60 \,cm$$ and $$AC = 61 \,cm$$
In $$\Delta ABC$$,
$$\Longrightarrow (AC)^2 = (AB)^2 + (BC)^2$$
$$\Longrightarrow (61)^2 = (60)^2 + (BC)^2$$
$$\Longrightarrow (BC)^2 = 3721 - 3600$$
$$\Longrightarrow BC = \sqrt{121}$$
$$\Longrightarrow BC = 11 \,cm$$
Hence, perimeter of the rectangle $$ABCD = 25(AB + BC)$$
$$\Longrightarrow 2 (60 + 11)$$
$$\Longrightarrow 2(71)$$
$$\Longrightarrow 142 \,cm$$
Question 4
1 / -0

A rectangular piece of dimensions $$3\,cm \times 2\, cm $$ was cut from a rectangular sheet of paper of dimensions $$6\, cm \times 5\, cm$$ (Fig). Area of remaining sheet of paper is

A
$$30 \, cm^2$$

B
$$36 \, cm^2$$

C
$$24 \, cm^2$$

D
$$22 \, cm^2$$

Solution

Option (c) is correct.
Given, Area of bigger rectangle $$=(6 \times 5)cm =30 \, cm^2$$
Area of smaller rectangle $$= (3 \times 2)cm = 6 \, cm^2$$
Therefore, area of remaining sheet of paper$$ = $$Area of bigger rectangle $$-$$ Area of smaller rectangle
$$=(30 -6)= 24 \, cm^2$$
Question 5
1 / -0

Write the correct answer from the given four options.
A square board has an area of 144 square units. How long is each side of the board?

A
11 units

B
12 units

C
13 units

D
14 units

Solution

Let $$a$$ be the length of the sides of the square.
Area of square board = $$a^2$$ $$=144$$
$$a=\sqrt{144} = 12$$ units
Question 6
1 / -0

(Distance between two dots is 1 cm)

Find the perimeter of Green Rectangle B

A
14 cm

B
16 cm

C
18 cm

D
12 cm

Solution
Question 7
1 / -0

(distance between two dots is 1 cm)

12 Red square can fit inside $$Green \,Rectangle \,A$$
12 Red square can fit inside $$Green \,Rectangle \,B$$

Which Rectangle has smaller perimeter

A
Green Rectangle B

B
Green Rectangle A

C
Both A and B have equal perimeter

D
Can not be determined

Solution
Question 8
1 / -0

Define perimeter of figure.

A
Space enclosed by a closed figure

B
Sum of all sides of figure

C
Length of boundary of figure

D
Both B and C

Solution
Question 9
1 / -0

What will be the area of the largest square that can be cut out of a circle of radius.

A
$$100\, cm^2$$

B
$$200\, cm^2$$

C
$$300\, cm^2$$

D
$$400\, cm^2$$

Solution

Given, radius of circle $$= 10\, cm$$

The diagonal of the square will be equal to the diameter of the circle.
Now, in right-angled triangle $$DAB$$,
$$\Rightarrow (BD)^2 = (AD)^2-(AB)^2$$
$$\Rightarrow (20)^2 =x^2+x^2$$
$$ \Rightarrow 2x^2=400$$
$$ \Rightarrow x^2 =200$$
Therefore, $$200\, cm^2$$ is the area of the largest square.
Question 10
1 / -0

(distance between two dots is 1 cm)

12 Red square can fit inside $$Green \,Rectangle \,A$$
12 Red square can fit inside $$Green \,Rectangle \,B$$

Which Rectangle has greater perimeter

A
Green Rectangle B

B
Green Rectangle A

C
both have equal perimeter

D
Can not be determined

Solution